1 Answer
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means "I'm supposed to read this book", like when a teacher assigns you the book to read as your homework.

Ich sollte das Buch lesen.

can mean both "I should read this book", as in "all things considered, I really should...", and "I was supposed to read this book", as in "What was my homework for today? Oh, right, I was supposed to..."

The form "ich solle" is subjunctive, which means you basically only need it to make reported speech sound formal: